Question: Hawkins Manufacturing Company produces connecting rods for 4- and 6-cylinder automobile engines using the same production line. The cost required to set up the production line to produce the 4-cylinder connecting rods is $2,000, and the cost required to set up the production line for the 6-cylinder connecting rods is $3,500. Manufacturing costs are $15 for each 4-cylinder connecting rod and $18 for each 6-cylinder connecting rod. There is no production on weekends, so on Friday the line is diassembled and cleaned. On Monday, the line must be set up to run whichever product will be produced that week. Once the line has been set up, the weekly production capacities are 6000 6-cylinder connecting rods and 8000 4-cylinder connecting rods. Let

x₄ = the number of 4-cylinder connecting rods produced next week

x₆ = the number of 6-cylinder connecting rods produced next week

s₄ = 1 if the production line is set up to produce the 4-cylinder connecting rods; 0 if otherwise

s₆ = 1 if the production line is set up to produce the 6-cylinder connecting rods; 0 if otherwise

a. Using the decision variables x₄ and s₄, write a constraint that sets next week's maximum production of the 4-cylinder connecting rods to either 0 or 8000 units.

b. Using the decision variables x₆ and s₆, write a constraint that sets next week's maximum production of the 6-cylinder connecting rods to either 0 or 6000 units.

c. Write a constraint that requires that production be set up for exactly one of the two rods.

d. Write the cost function to be minimized.